Introduction to isolated horizons in numerical relativity

We present a coordinate-independent method for extracting the mass ${(M}_{\Delta })$ and angular momentum ${(J}_{\Delta })$ of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. Assuming that the spatial hypersurfaces used in a given numerical simulation are such that apparent horizons exist and have been located on these hypersurfaces, we show how $J_{\Delta }$ and $M_{\Delta }$ can be determined in terms of only those quantities which are intrinsic to the apparent horizon. We also present a numerical method for finding the rotational symmetry vector field (required to calculate $J_{\Delta })$ on the horizon.